Insulation PF Testing of Trafo

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INSULATION POWER FACTOR TESTING of POWER TRANSFORMERS Oleh W. Iwanusiw, consultant Eltel Industries, Bangalore, India RESUME This paper discusses the dissipation factor measurements that can be carried out on the insulation of power transformers during routine maintenance procedures. This presentation includes a definition of terms, outlines measurements and calculations to be performed and discusses the interpretation of test results. INTRODUCTION & DEFINITIONS Capacitance. Capacitance of a system is defined by the magnitude of charge that it can store at a given voltage. The charge is proportional to the area of the conductive plates, the dielectric constant of the insulating material between the plates and inversely proportional to the distance between them (Figure 1). Vacuum and air have a dielectric constant of 1 and all other insulating materials have a dielectric constant larger than 1. Power Factor, Dissipation Factor, Tan Delta. The Power Factor in a circuit is defined as the ratio of power to volt-amperes (W/ VA). Power Factor is also defined as the cosine of the angle between the voltage and current in a circuit, with the angle typically referred to as ‘theta’. This angle is typically very close to 90 degrees for capacitive (insulation) circuits. Dissipation Factor is defined as the ratio of power to reactive volt-amperes (W/VAr) in a circuit. The Dissipation Factor is equal to the tangent of ‘Delta’, where ‘Delta’ is the angle of 90 O minus ‘theta’ (Figure 2 for clarification). Figure - 1 Capacitance - 1-

Transcript of Insulation PF Testing of Trafo

  • INSULATION POWER FACTOR TESTINGof

    POWER TRANSFORMERS

    Oleh W. Iwanusiw, consultantEltel Industries, Bangalore, India

    RESUME

    This paper discusses the dissipation factor measurements that can be carried outon the insulation of power transformers during routine maintenance procedures. Thispresentation includes a definition of terms, outlines measurements and calculations to beperformed and discusses the interpretation of test results.

    INTRODUCTION & DEFINITIONS

    Capacitance.

    Capacitance of a system is defined by the magnitude of charge that it can store at agiven voltage. The charge is proportional to the area of the conductive plates, the dielectricconstant of the insulating material between the plates and inversely proportional to thedistance between them (Figure 1). Vacuum and air have a dielectric constant of 1 and allother insulating materials have a dielectric constant larger than 1.

    Power Factor, Dissipation Factor, Tan Delta.

    The Power Factor in a circuit is defined as the ratio of power to volt-amperes (W/VA). Power Factor is also defined as the cosine of the angle between the voltage andcurrent in a circuit, with the angle typically referred to as theta. This angle is typicallyvery close to 90 degrees for capacitive (insulation) circuits.

    Dissipation Factor is defined as the ratio of power to reactive volt-amperes(W/VAr) in a circuit. The Dissipation Factor is equal to the tangent of Delta, whereDelta is the angle of 90O minus theta (Figure 2 for clarification).

    Figure - 1Capacitance

    - 1-

  • For practical insulation circuits, where theta is larger than 85 O, the PowerFactor and the Dissipation Factor are numerically the same.

    Grounded Specimen Test.

    The Grounded Specimen Test (GST) is referred to as the measurement of aninsulation sample that has one of its terminals grounded. To conduct a GST test, themeasuring circuit of the instrument used must be ungrounded to make the measurementpossible. As most pieces of electric power system equipment is grounded, the groundedspecimen test must be used if the equipment is to be tested in the installed condition. GSTis therefore the most important and most frequently used test. Most up-to-date testequipment also offer a grounded specimen test with guard-GSTg. This connection allowsone to measure one component of a multi-component, grounded, insulation system.

    Ungrounded Specimen Test.

    The Ungrounded Specimen Test (UST) is referred to as the test of an insulationsample that is not grounded. This test configuration automatically provides a guardconnection that can be used effectively to measure only one component out of a multi-component insulation system. The UST is of great advantage as its guard connection isalso ground. This means that anything that is grounded in a UST measurement isautomatically excluded from the measurement.

    Cold Guard / Hot Guard Measurements.

    Cold guard or hot guard connections refer to the potential of the guard terminalor connection. When the guard potential is at or near ground potential, then it is referredto as a cold guard. The UST configuration, providing a guard that is also a ground, istherefore a cold guard connection.

    When using the GST connection, the guard potential may be at or near groundpotential (cold guard), or at the test potential (hot guard), depending on the configurationof the test equipment. In practice, the cold guard configuration is typically used in testequipment operating at higher voltage, and the 'hot guard is used in test equipmentoperating at low voltage. This is so because of safety considerations, where test personnelmay inadvertently mistake the hot guard terminal as being at ground potential.

    Figure - 2Power Factor / Dissipation Factor

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  • The primary advantage of the hot guard connection is that it is more tolerant ofinterference that is typically encountered in a field test situation. See Figure 3 for UST,GST, Cold Guard & Hot Guard connections. It must be pointed out that typical measuringinstruments will feature either the Hot Guard or the Cold Guard connection, not both.

    Power Loss.

    Power loss or watts loss is the colloquial term often used in connection withinsulation measurements and refers to the power being dissipated in the insulation. It isthe product of the test voltage, the test current and the cosine of theta. It is typically usedfor test specimen that have small capacitance and as a result the power factor (tan Delta)of the test circuit is rather high. The power loss is also a very convenient number whenchecking the accuracy of measurements.

    Equivalent 10kV value.

    Capacitance, Power Factor and Dissipation Factor are terms that are not affectedby changes in test voltage. They can be measured without having to set the test voltageprecisely. The power loss or watts loss values depends on the test voltage (proportionalto the square of the test voltage) and therefore needs to be corrected to a reference voltage.10 kV has become the preferred reference voltage when testing high voltage electricpower equipment. A reference voltage of 2.5 kV is often used when testing equipmentrated at distribution or lower voltages.

    COMPONENTS REQUIRING TESTING

    General Comments.

    It must be pointed out that a single measurement on a transformer typicallyrepresents several components within the transformer. For this reason it is necessary toperform certain simple calculations that will separate out individual components forcomparison purposes. A good example of this is the situation where the measurement ofa transformer includes the winding capacitance and the capacitance of the bushing orbushings. If one wishes to examine only the quality of the winding insulation, one mustsubtract the capacitance and loss of the bushings from the overall measurement.

    1. UST = GUARD = GROUND, COLD GUARD2. GST = LO = GROUND, COLD GUARD

    3. GST = HI = GROUND, HOT GUARD

    Figure - 3 Transformer Ratio Arm Bridge

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    GUARD

  • The winding insulation of three phase transformers is typically measured togetherfor all three phases. The reason for this is that the windings are interconnected and it isimpractical to separate them for the test. It is often possible to separately measure thecapacitance of each winding in the factory before the bushings are installed and connected.

    Bushings.

    The measurement of bushings is rather simple, provided that they are equippedwith a test tap or a Cap-Tap as it is often referred to. All modern high-voltage bushingsare equipped with this feature. If the bushing is not equipped with the test tap, thenone must resort to other techniques to evaluate the condition of the bushing. Using thehot collar method is one such technique.

    The actual measurement of a bushing is typically done using the UST connection,and the test tap may be connected to the test voltage or to the measuring lead. Theimportant measurement is the Tap-to-conductor capacitance. When in service, it hasthe system voltage applied to it. The Tap-to-ground capacitance is shorted out duringnormal operation of the equipment and is typically not measured.

    Two Winding Transformers.

    The simplified schematic diagram of a two winding transformer is shown inFigure 4. It consist of three components, namely:

    k The high voltage winding to ground capacitance (Ch-g),k The high voltage to low voltage winding capacitance (Ch-l),k The low voltage winding to ground capacitance (Cl-g).

    The Ch-g and Cl-g measurements include the capacitance of the appropriatebushings. The Ch-g measurement includes the capacitance of the HV bushing and theCl-g measurement includes the LV bushing. It is IMPORTANT to note that the Ch-lmeasurement does not include the bushings as the capacitance of the bushings is connectedto ground and is automatically removed from the measurement in the UST connection.

    Three Winding Transformers.

    The simplified schematic diagram of a three winding transformer is shown inFigure 5. Labelling the windings in this transformer as high voltage, low voltage andtertiary, the schematic consists of six components, namely:

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    Figure - 42 Winding Transformers

  • k The high voltage to low voltage winding capacitance (Ch-l),k The high voltage to tertiary winding capacitance (Ch-t),k The low voltage to tertiary winding capacitance (Cl-t),k The high voltage winding to ground capacitance (Ch-g),k The low voltage winding to ground capacitance (Cl-g), andk The tertiary winding to ground capacitance (Ct-g).

    Similar to the two winding example, all the capacitances between the windings and ground(Ch-g, Cl-g, Ct-g) include the capacitances of the appropriate bushings. The capacitanceand loss of the bushings need to be subtracted from the measurement if only the losses inthe winding are to be examined. Again, it is IMPORTANT to point out again that theinterwinding capacitances (Ch-l, Cl-t & Ct-h) do not include the capacitances of theassociated bushings.

    Insulating Oil.

    Testing of insulating oil requires a oil test vessel in addition to the power factortest set. The vessel, or oil test cell is typically a three-electrode system which providesguarding against surface leakage. This is important as the test cell capacitance is smalland even small leakage may cause substantial errors in measurement.

    Unless the sampled oil is to be subjected to numerous other tests, it is best todirectly fill the power factor test cell from the sampling facility provided on the testedpower transformer. One must assure that the test cell is clean and it is a wise precautionto bleed the sampling tube to assure a representative sample.

    Oil tests in the shop or laboratory would be carried out at room temperature (20O C)as well as at an elevated temperature of 90O or 100O C. Tests at these two temperaturesprovides much more insight into the characteristics and quality of the oil encountered.

    Testing of oil in the field is typically limited to testing at whatever temperatureprevails at the test site. As the temperature may vary widely, it must be measured so thattemperature correction can be applied to the results.

    PREPARATION for TESTING

    Isolation.

    Before attempting to connect test equipment to a transformer, one must makecertain that it is fully isolated and grounded. The best isolation is at the terminals (bushings)of the transformer and not at the end of a length of bus or cable. The reason for this is that

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    Note : C H- G, CL -G and CT-G include capacitances of Associated bushings,

    Figure - 53 Winding Transformers

  • every meter of bus attached to the transformer will be instrumental in attracting capacitiveinterference current from energised equipment in the station. As the accuracy of powerfactor measurement is inversely proportional to the amount of interference, it is prudentto have as little interference as possible so that the results will be most accurate andreproducible.

    Another reason for isolating the test specimen at its terminals is that this avoids measuringthe losses associated with the cable or bus (insulators) that may be attached to it.

    Cleaning.

    It is prudent to clean all insulators on a transformer prior to any measurement.This is important in coastal areas where salt may settle on insulators or in areas of heavyindustrial pollution. This is especially important when the transformer bushings are notequipped with test taps and have to be measured using collars.

    Recording of Information.

    It is very important to record all information that is relevant to the test. Suchinformation, in addition to all test equipment readings, must include:

    k The location of the station and the position of the equipment within the station.k Make, Type and Serial Number of equipment tested.k Condition of the test transformer regarding its temperature, oil level, tap

    position and mechanical appearance.k The prevailing ambient weather conditions including Temperature, Humidity,

    Wind direction and velocity.

    It is desirable to record ALL the information the test equipment provides. Sometest equipment provides readings of capacitance, dissipation factor as well as watts loss.Recording all of this information makes calculations and double checking of thereadingseasier.

    It a very good practice to standardise on a suitable test report format that willguide the test personnel in providing all of the desired data.

    Given in the APPENDIX are several procedures that can be used to test theinsulation power factor (dissipation factor) of power transformer insulation.

    INTERPRETATION of TEST RESULTS

    General discussion.

    Interpreting the results of Dissipation/Power Factor test is as demanding as is themeasurement process. The interpretation is especially difficult in the beginning when onedoes not have much history on the equipment - transformer being evaluated. In the end onemust admit that the evaluation of test results is as much art as it is science.

    The interpretation process involves comparing the results on hand with previousresults, or with the results from similar equipment.

    Temperature corrections.

    It must be recognised that the losses of most electrical insulation are temperaturesensitive. The temperature sensitivity depends on the materials used in the insulationsystem, such as paper, fibreboard, oil etc. Different sources of paper or oil will exhibitdifferent temperature characteristics.

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  • Before any comparison or interpretation can take place, the readings must becorrected to a reference temperature of 20O C. The use of a particular temperature correctiontable in itself may be an important decision as there are many different temperaturecorrection curves available and used in the industry. There are different tables for differentinsulating oils, one North American and the other European. There are different tablesfor different types of insulation systems within the transformer. There are also differenttypes of tables for different types and makes of bushings.

    One must assure himself that the temperature correction one is using indeed appliesto the equipment being tested. One way of avoiding the reliance on corrections is to testthe equipment approximately at the same time of the year, when the ambient temperatureand the loadings may be similar.

    Comparison with factory tests, precious readings

    When comparing to factory readings or to previous readings, one is looking for abruptchanges as well as for rending. Abrupt changes are typically investigated immediately,while the trends are watched for limits that indicate the necessity of corrective action.Dissipation Factor limits for various pieces of equipment have been determined frompractice and are used as a guide for corrective action.

    Some guidelines.

    As a guide for those starting out in the insulation Dissipation Factor test field, onecan assemble a table that can be used as a guide. This table is made up of informationpublished by a variety of individuals as well as associations working in the field.

    Dissipation Factor at 20O C.

    Rating New Used QuestionableEquipment Equipment

    HV Oil 0.0005 0.005 0.01

    LV Oil 0.001 0.01 0.03

    400 kV 0.003 0.006 0.012

    The above table must not be used blindly and without considering the occurrenceof over voltages and surges on the system as well as the consequences of failure of theequipment while in service. There is no guarantee that Dissipation Factor values lowerthen those listed will not result in failure of the equipment.

    APPENDIX

    CONDUCTING THE MEASUREMENTS

    Whenever making measurements, it is important to make more measurementsthan the bare minimum. This allows one to double check all the results on the spot andavoid repeats.

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    To allow for convenient measurement with the fewest possible connections, manycommercial test sets provide two measuring leads and a variety of test configurations. Withtwo measuring leads, labelled as Yellow (Y) and Blue (B), the Ground connection labelled asG, and the high voltage lead as Red (R), the following measurements are possible:

    1. UST R - (Y+B)2. UST R - B3. UST R - Y4. GST R - (G+Y+B)5. GSTg R - G6. GSTg R - (Y+G)7. GSTg R - (B+G)

    The listed measurements offer duplication and therefore allow one to check the results. It issuggested that all of these, plus even additional readings be taken to ascertain good results.

    Connecting the Test Equipment.

    To promote safety, it is recommended that the transformer to be tested be isolatedand grounded by the operating personnel, using the normal utility practices. The powerfactor test equipment would then be connected to the transformer by the test personnel,including any shorting of windings etc. Now the grounds would be removed and thetesting with commence.

    As was recommended in the earlier section, it is recommended that all possiblereadings be taken as cross checking these readings will provide a measure of accuracyand repeatability in the measuring process. All the readings are to be entered on preparedforms or alternatively in work books.

    When changing connections, it is recommended to first ground the testtransformer, change the connections, then remove the grounds and continue testing.

    Two Winding Transformer.

    Generally speaking, the test connections listed below are designed to provide allthe desired measurements with the fewest test set ups. The actual number of connectionswill depend on the number and ratings of bushings installed on the transformer.

    Example No. 1.

    This first example is that for a transformer with one HV bushing and intendedfor line to neutral installation on the HV side.

    Test connection No. 1.

    a. Remove the grounding strap from the neutral bushing of the HV winding.

    b. Short the HV winding; short the LV winding.

    c. Connect the RED lead to the HV bushing.d. Connect the YELLOW lead to the LV bushing.e. Connect the BLUE lead to the HV bushing Cap Tap.f. Remove grounds before proceeding with measurements.

    Measure all seven (7) possible combinations on the test set:

    1. (1) R-Y Ch-l HV to LV capacitance.2. (2) R-B Ch-bushing, Bushing capacitance only.3. (3) R-(Y+B) (Ch-l)+(Ch-bushing)

  • 4. (4) R-(Y+B+G) (Ch-l)+(Ch-bushing)+(Ch-g)5. (5) R-G Ch-g H to Ground capacitance only.6. (6) R-(Y+G) (Ch-l)+(Ch-g)7. (7) R-(B+G) (Ch-bushing)+(Ch-g)

    Note that this sequence measures ALL the capacitances associated with the HVwinding, including the bushing. Combinations of readings allow operator to double checkindividual readings.

    Test connection No. 2.

    g. Move the RED lead to the LV bushing.h. Move the YELLOW lead to the HV bushing.i. Disconnect the BLUE lead.

    Measure the following 3 configurations:

    8. (2) R-Y Cl-h HV to LV capacitance.9. (5) R-G Cl-g Capacitance LV to Ground.10. (6) R-(Y+G) (Cl-h)+(Cl-g)

    This example measures the 4 primary values (Ch-l; Ch-g; Ch-bushing; Cl-g)using 10 measurements. Each primary value is measured separately as well as incombination, two or mere times.

    Example No. 2.

    Two winding transformer with two HV bushings.

    Test connection No. 1.

    a. Short the HV winding; short the LV winding.b. Connect the RED lead to the HV winding.c. Connect the YELLOW lead to the LV winding.d. Remove grounds before proceeding with measurements.

    Measure the following 3 configurations:

    1. (1) R-Y Ch-l HV to LV capacitance.2. (5) R-G Cl-g HV to ground capacitance.3. (6) R-(Y+G) (Ch-l)+(Ch-g)

    Set up No. 2.

    e. Move the YELLOW lead to the HV1 bushing tap.f. Connect the BLUE lead to HV2 bushing tap.

    Measure the following 3 configurations:

    4. (1) R-Y C1-bushing.5. (2) R-B C2-bushing.6. (3) R-(Y+B) C1+C2-bushings.

    Additional measurements can be taken using this set up.

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  • - 10 -

    Set up No. 3.

    g. Move the RED lead to the LV winding.h. Move the YELLOW lead to the HV winding.

    7. (1) R-Y Cl-h HV to LV capacitance.8. (5) R-G Cl-g LV to ground capacitance.9. (6) R-(Y-G) (Cl-h)+(Cl-g)

    The No. 2 example sequence measures the 5 primary values using 9 measurements.Each capacitance is measured separately as well as in combination.

    Additional examples can be cited for three phase, two winding, transformers. Thecomplication here is that there is one or two additional bushings to deal with on the HV side.No additional complications exist if the bushings on the LV side are of low voltage rating. Ifthe LV winding is of high voltage and has bushings with cap taps, then these need to be dealtwith in the same fashion as the bushings on the HV side.

    Three Winding Transformer.

    For those who considered the two winding transformer example to be rather tedious, theywill be thrilled by all the readings that are possible and indeed suggested for a three windingsingle phase transformer.

    Assuming that there are bushings to be tested on the HV and Tertiary windings of thetransformer, then the procedure below is suggested:

    Test connection No. 1.

    a. Short the HV winding; short the Tertiary winding; short the LV winding.b. Connect the RED lead to the HV winding.c. Connect the YELLOW lead to the LV winding.d. Connect the BLUE lead to the T winding.e. Remove grounds before proceeding with measurements.

    Measure the following 7 configurations:

    1. (1) R-Y Ch-l HV to LV capacitance.2. (2) R-B Ch-t HV to T capacitance.3. (3) R-(Y+B) (Ch-l)+(Ch-t)4. (4) R-(Y+B+G) (Ch-l)+(Ch-t)+(Ch-g)5. (5) R-G Ch-g H to Ground capacitance.6. (6) R-(Y+G) (Ch-l)+(Ch-g)7. (7) R-(B+G) (Ch-t)+(Ch-g)

    Test connection No. 2.

    f. Move the YELLOW lead to the HVa bushing tap.g. Move the BLUE lead to HVb bushing tap.

    Measure the following 3 configurations:

    8. (1) R-Y HVa-bushing.9. (2) R-B HVb-bushing.10. (3) R-(Y+B) HVa+HVb-bushings.

    Test connection No. 3.

    h. Move the YELLOW lead to the HVc bushing tap.i Move the BLUE lead to HVn bushing tap (if applicable).

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    Measure the following 3 configurations:

    11. (1) R-Y HVc-bushing.12. (2) R-B HVn-bushing (if applicable).13. (3) R-(Y+B) HVc+HVn-bushings (if applicable).

    Test connection No. 4.

    j. Move the RED lead to the Tertiary winding.k. Leave the YELLOW lead on the LV winding.l. Move the BLUE lead to the HV winding.

    Measure the following 7 configurations:

    14. (1) R-Y Ct-l Tertiary to LV capacitance.15. (2) R-B Ct-h Tertiary to HV capacitance.16. (3) R-(Y+B) (Ct-l)+(Ct-h)17. (4) R-(Y+B+G) (Ct-l)+(Ct-h)+(Ct-g)18. (5) R-G Ct-g Tertiary to Gr. capacitance.19. (6) R-(Y+G) (Ct-l)+(Ct-g)20. (7) R-(B+G) (Ct-h)+(Ct-g)

    Test connection No. 5.

    m. Move the YELLOW lead to the Ta bushing tap.n. Move the BLUE lead to Tb bushing tap.

    Measure the following 3 configurations:

    21. (1) R-Y Ta-bushing.22. (2) R-B Tb-bushing.23. (3) R-(Y+B) Ta+Tb-bushings.

    Test connection No. 6.

    o. Move the YELLOW lead to the Tc bushing tap.p. Move the BLUE lead to Tn bushing tap (if applicable).

    Measure the following 3 configurations:

    24. (1) R-Y Tc-bushing.25. (2) R-B Tn-bushing (if applicable).26. (3) R-(Y+B) Tc+Tn-bushings (if applicable).

    Test connection No. 7.

    q. Move the RED lead to the LV winding.r. Move the YELLOW lead to the Tertiary winding.s. Leave the BLUE lead to the HV winding.

    Measure the following 7 configurations:

    27. (1) R-Y Cl-t LV to Tertiary capacitance.28. (2) R-B Cl-h LV to HV capacitance.29. (3) R-(Y+B) (Cl-t)+(Cl-h)30. (4) R-(Y+B+G) (Cl-t)+(Cl-h)+(Cl-g)31. (5) R-G Cl-g LV to Ground capacitance.32. (6) R-(Y+G) (Cl-t)+(Cl-g)33. (7) R-(B+G) (Cl-h)+(Cl-g)

  • - 12 -

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    The above test sequence is designed to measure the 6 capacitance values associated with a threewinding transformer plus up to eight bushings. The sequence uses seven different connections and 33measurements. Similarly to the previous examples, each value is measured at least twice using differentconnections or a combination of connections. This procedure allows for complete verification of resultsbefore any action is taken.

    Checking of Test Results.As was explained earlier in the text, the suggested procedures measure the various capacitance

    values two or more times in order to assure that the results are correct and valid. This is accomplishedin the following way:

    1. A full sequence of 7 tests in a connection allows one to check the following: #1 = #2 + #3; #4 =#1 + #2 +#5; #6 = #2 + #5; and #7 = #3 + #5. A partial sequence allows for partial checking.

    2. The winding to winding capacitance values are always measured twice, once from each winding.This allows for easy comparisons, as Ch-l should equal Cl-h. Similarly for other windings.

    These calculations are easiest to carry out if the data is presented in capacitance and loss. Thepicofarads (microfarads) and watts (milliwatts) can be added directly to verify readings.

    If the data is presented in capacitance and dissipation factor, then the calculation requires a fourfunction calculator, as the dissipation factor must be weighted according to the capacitance value. Thecapacitance values can be added directly as before.

    Interference considerations.One of the most difficult situations to contend with is the presence of interference during the

    measurement process. As was explained earlier, some measurement connections are more sensitive tointerference than others. Thus, for example, a UST connection is less bothered by interference than aGST connection. Also, an instrument featuring a HOT GUARD in the GST connection is less sensitiveto interference than is an instrument featuring a COLD GUARD.

    It must be pointed out that even in the UST connection, which typically can be configured twodifferent ways on a test sample, will perform differently on the two connections. It all depends on howthe interference is coupled to the test specimen.

    Thus, for example, when measuring a bushing using the cap-tap, it is usually desirable to apply thetest voltage to the HV terminal and connect the cap-tap to the measuring lead. This is because interferenceis typically coupled to the HV terminal and not to the cap-tap connection.

    Most test equipment provides some means of rejecting or cancelling the encountered interference.This is typically done by injecting a current that is equal to the interfering current, but of oppositepolarity, into the test circuit. This configuration is not perfect as the encountered interference varieswith variations in the system voltage. If the system voltage goes up, so does the amount of interference.Typical interference cancellation schemes are not capable of following line voltage swings so therealways is a residual quantity of interference that cannot be eliminated.

    The result of residual interference vary. At times the readings fluctuate and the instrument is difficult tobalance. At times it will result in readings that are low in dissipation factor, or even exhibit a negative value.